High Spy wrote: ↑Sun May 01, 2022 8:16 pm

Res Ipsa wrote: ↑Sun May 01, 2022 7:54 pm

If we consider the order of the flips, aren’t all possible outcomes equally likely?

Yes, each expected outcome is 1/32.

OK, so thinking about HTHTH,

If we choose to describe it as the result of each flip in the order they occurred, the outcome is no less expected than any other outcome — all outcomes are equally improbable, but if we flip the coins, there is a 100% chance that one of those improbable outcomes will happen.

But if we choose to describe the same coin flips this way: three heads and two tails, the probability rises from 1/32 to 10/32 — around 1/3.

If we choose to describe the same coin flips as two of one result and three of another, the probability soars to 20/32 — almost 2/3.

But If we describe the same set of flips as alternating results, the probability falls to 1/16.

All of these descriptions of the results of the five flips are accurate. But which one we choose to use changes the probability from 1/32 to 1/16 to 1/3 to 2/3.

If we are trying to decide whether the result of the flips has some significance beyond random chance, which description is correct and why?